Answer:
y = 8·√3
Step-by-step explanation:
From the drawing of the right triangle, we have;
The length of the opposite leg to the given 60° (reference) angle = 12
The length of the adjacent leg to given 60° (reference) angle = x
The length of the hypotenuse side = y
By trigonometric ratios, we have;
[tex]sin(Reference \, Angle) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
Therefore, we have;
[tex]sin(60^\circ) = \dfrac{12}{y}[/tex]
From the value of sin(60°), we have;
[tex]sin(60^\circ) = \dfrac{\sqrt{3} }{2}[/tex]
[tex]\therefore y= \dfrac{12}{sin(60^\circ) } = \dfrac{12}{\dfrac{\sqrt{3} }{2} } = \dfrac{2 \times 12 \times \sqrt{3} }{{{3} } } = \dfrac{24 \times \sqrt{3} }{{{3} } } = 8 \cdot \sqrt{3}[/tex]
y = 8·√3
[tex]\left(x= \dfrac{12}{tan(60^\circ) } = \dfrac{12}{{\sqrt{3} } } = 4\cdot \sqrt{3} \right)[/tex]
